Unreplicated split-plot mixture designs and statistical models for optimizing mobile chromatographic phase and extraction solutions for fingerprint searches

An unreplicated composite mixture design and statistical model are proposed to simultaneously optimize mixture systems having interaction effects. A split-plot design is made up of standard mixture designs at both the main-plot and sub-plot levels. The model is obtained by multiplying Scheffé mixture models for each mixture system. Equations for the coefficients of a special cubic-special cubic balanced model are presented as well as their standard errors for both random and split-plot design structures. The design is applied to the simultaneous optimization of both mobile phase chromatographic mixtures and extraction mixtures for the Baccharis milleflora (Less.) DC plant. The whole-plot extraction mixtures contained varying proportions of ethanol, ethyl acetate and dichloromethane in a simplex centroid design. The sub-plot reversed phase chromatographic mixtures also followed a simplex centroid design in varying proportions of methanol, acetonitrile and a methanol–acetonitrile–water 15:15:70% v/v mixture. Assuming random execution of experiments normal probability graphs for the coefficients of a saturated model were plotted to make an initial determination of significant model coefficients. These parameters were then refined using a reduced model containing a split-plot error structure. Two models were developed to estimate the number of peaks observed using the chromatographic detector at both 210 and 254 nm wavelengths. The significant model coefficients are interpreted physically in terms of interacting linear, curvature and special cubic effects.